Jinsong Huang

Influence of Spatial Variability on Slope Reliability Using 2-D Random Fields

The paper investigates the probability of failure of slopes using both traditional and more advanced probabilistic analysis tools. The advanced method, called the random finite-element method, uses elastoplasticity in a finite-element model combined with random field theory in a Monte-Carlo framework. The traditional method, called the first-order reliability method, computes a reliability index which is the shortest distance (in units of directional equivalent standard deviations) from the equivalent mean-value point to the limit state surface and estimates the probability of failure from the reliability index. Numerical results show that simplified probabilistic analyses in which spatial variability of soil properties is not properly accounted for, can lead to unconservative estimates of the probability of failure if the coefficient of variation of the shear strength parameters exceeds a critical value. The influences of slope inclination, factor of safety (based on mean strength values), and cross correlation between strength parameters on this critical value have been investigated by parametric studies in this paper. The results indicate when probabilistic approaches, which do not model spatial variation, may lead to unconservative estimates of slope failure probability and when more advanced probabilistic methods are warranted.

Probabilistic Analysis of Coupled Soil Consolidation

Coupled Biot consolidation theory was combined with the random finite-element method to investigate the consolidation behavior of soil deposits with spatially variable properties in one-dimensional (1D) and two-dimensional (2D) spaces. The coefficient of volume compressibility ( mv ) and the soil permeability (k) are assumed to be lognormally distributed random variables. The random fields of mv and k are generated by the local average subdivision method which fully takes account of spatial correlation, local averaging, and cross correlations. The generated random variables are mapped onto a finite-element mesh and Monte Carlo finite-element simulations follow. The results of parametric studies are presented, which describe the effect of the standard deviation, spatial correlation length, and cross correlation coefficient on output statistics relating to the overall “equivalent” coefficient of consolidation. It is shown that the average degree of consolidation defined by excess pore pressure and settlemen...

On the reliability of earth slopes in three dimensions

The paper investigates the probability of failure of two-dimensional and three-dimensional slopes using the random finite-element method (RFEM). In this context, RFEM combines elastoplastic finite-element algorithms with random field theory in a Monte Carlo framework. Full account is taken of local averaging and variance reduction over each element, and an exponentially decaying (Markov) spatial correlation function is incorporated. It is found that two-dimensional probabilistic analysis, which implicitly assumes perfect spatial correlation in the out-of-plane direction, may underestimate the probability of failure of slopes.

Characterizing Natural-Fracture Permeability From Mud-Loss Data

Original SPE manuscript received for review 20 October 2009. Revised manuscript received for review 29 March 2010. Paper (SPE 139592) peer approved 25 May 2010. Summary Liétard et al. (1999, 2002) have provided important insight into the mechanism and prediction of transient-state radial mud invasion in the near-wellbore region. They provided type curves describing mud-loss volume vs. time that allow the hydraulic width of natural fractures to be estimated through a curve-matching technique. This paper describes a simpler and more direct method for estimating the hydraulic width by the solution of a cubic equation, with input parameters given by the well radius rw, the overpressure ratio p/ y, and the maximum mud loss volume (Vm)max.

On the efficient estimation of small failure probability in slopes

The random finite element method (RFEM) combines the random field theory and finite element method in the framework of Monte Carlo simulation. It has been applied to a wide range of geotechnical problems such as slope stability, bearing capacity and the consolidation of soft soils. When the RFEM was first developed, direct Monte Carlo simulation was used. If the probability of failure (pf) is small, the direct Monte Carlo simulation requires a large number of simulations. Subset simulation is one of most efficient variance reduction techniques for the simulation of small pf. It has been recently proposed to use subset simulation instead of direct Monte Carlo simulation in RFEM. It is noted, however, that subset simulation requires calculation of the factor of safety (FS), while direct Monte Carlo requires only the examination of failure or non-failure. The search for the FS in RFEM could be a tedious task. For example, the search for the FS of slope stability by the strength reduction method (SRM) usually requires much more computational time than a failure or non-failure checking. In this paper, the subset simulation is combined with RFEM, but the need for the search of FS is eliminated. The value of yield function in an elastoplastic finite element analysis is used to measure the safety margin instead of the FS. Numerical experiments show that the proposed approach gives the same level of accuracy as the traditional subset simulation based on FS, but the computational time is significantly reduced. Although only examples of slope stability are given, the proposed approach will generally work for other types of geotechnical applications.

Risk assessment in geotechnical engineering: stability analysis of highly variable soils

The paper will review the state-of-the-art in the use of finite element methods for modeling geotechnical engineering problems involving non-typical geometries and highly variable soil properties. Examples will focus on slope stability analyses in which traditional limit equilibrium methods, and even well-established probabilistic methodologies may lead to misleading results.

Buried footings in random soils: comparison of limit analysis and finite element analysis

The limit analysis and the finite element method are powerful tools for analysing the bearing capacity of foundations. Previous research mainly focused on the foundations in uniform soils. In realistic conditions, soil properties are always varying spatially due to complex physical, chemical, and biological process in earth evolution. This paper investigates the bearing capacity and failure mechanism of footings buried at various depths in clays with spatially variable distribution of undrained shear strength using the lower bound limit analysis, the upper bound limit analysis, and the finite element analysis. Results show that the bearing capacity increases with increasing buried depths in spatially random soils, which is the same as in the uniform soils. The bearing capacity factors calculated using the finite element method, the lower bound limit analysis, and the upper bound limit analysis for a footing in spatially varied soils are all smaller than the corresponding values in uniform soils. The majority of the bearing capacity factors obtained from the finite element method is bounded by those obtained from the lower bound and the upper bound limit analysis. The shear planes show a clearly unsymmetrical manner in spatially varied soils using the three methods, which is different from the symmetrical shear plane in uniform soils.

Comparison of slope reliability methods of analysis.

Reliability tools have been applied to slope stability analysis more than any other geotechnical application on account of the readily understood concept of probability of failure as an alternative or complement to the traditional factor of safety. Probabilistic slope stability methods in the literature are reviewed. Particular attention is focused on the ability of the methods to correctly model spatially varying soil properties. A benchmark slope is reanalyzed and conclusions reached about their suitability for meaningful and conservative prediction of slope reliability.

Stochastic Evaluation of Hydraulic Hysteresis in Unsaturated Soils

AbstractThe effect of hydraulic hysteresis on the analysis of seepage in unsaturated soils is evaluated stochastically. A hysteretic seepage model is introduced by coupling the governing Richards equation with a hysteretic soil-water retention curve. The first-order second-moment (FOSM) method is used to study the effect of uncertainty in the input parameters on the one-dimensional seepage behavior of a soil column. A performance function is established in terms of the capillary-barrier effect in a multilayered capillary soil cover system. The contribution of variations in the flux at the top boundary on the performance of the soil cover is first investigated with both the traditional nonhysteretic model (NHM) and the hysteretic model (HM). Comparisons show that the HM model is comparatively conservative in the seepage analysis of unsaturated soils and that stochastic seepage behavior is closely associated with the hydraulic history of the soil. In addition, the effects of key input parameters in the HM m...

Probabilistic Finite Element Analysis of a Raft Foundation Supported by Drilled Shafts in Karst

The paper describes probabilistic analyses performed as part of a large expansion to an existing cement manufacturing plant. A raft supported by drilled shafts was proposed for the project, but during installation, significant slurry and concrete loss began to occur indicating numerous voids existed in what was previously considered competent limestone bedrock. Since the possibility of voids, especially at the shaft tip, could serious reduce the shaft capacity, a probabilistic Monte Carlo 3D finite element simulation was proposed for the most heavily loaded raft foundation. The purpose of the simulation was to determine the probability of adverse performance, giving guidance as to whether any remedial measures (e.g., additional structural elements or thickened raft) might be required.